The present invention relates to system identification methods, and more particularly, to a time-varying system identification method at a high speed in real time by using a fast algorithm for modified H∞ filters developed based on a new H∞ evaluation criterion.
In general, system identification is to estimate a mathematical model (a transfer function, an impulse response, or the like) of a system input-and-output relationship according to the input-and-output data. Typical applications thereof include echo cancellers in international communications, automatic equalizers in data communications, echo cancellers in acoustic systems, sound-field reproduction, and active noise control in vehicles. Details are written in “Digital Signal Processing Handbook”, the Institute of Electronics, Information and Communication Engineers, 1993, or the like.
(Basic Principle)
FIG. 14 shows a configuration for system identification. This system includes an unknown system 1 and an adaptive filter 2. The adaptive filter 2 has an FIR digital filter 3 and an adaptive algorithm 4.
One case which uses an output error method to identify the unknown system 1 will be described below. Here, uk indicates an input to the unknown system 1, dk indicates the output of the system, which is a signal to be obtained, and d^k indicates the output of the filter. (A mark “^” means an estimated value and should be placed above characters, but it is placed at the upper right of the characters for input convenience. This notation may be used through the present specification.)
Since an impulse response is generally used as a parameter of an unknown system, the adaptive filter adjusts a coefficient of the FIR digital filter 3 by the adaptive algorithm such that an evaluation error ek=dk−d^k in the figure is minimized.
FIG. 15 shows the structure of an impulse-response adjustment mechanism.
Here, as an example of adaptive algorithm, the following LMS algorithm (least mean square algorithm) is widely used because of its computational simplicity.
[LMS Algorithm]ĥk+1=ĥk+μuk(yk−ukTĥk)  (1)where,ĥk=[ĥ0[k], . . . ,ĥN−1[k]]T, uk=[uk, . . . , uk−N+1]T, μ>0  (2)Generally, Kalman filters, which converges quickly, are suitable for identifying a time-varying system.[Kalman Filter]{circumflex over (x)}k|k={circumflex over (x)}k|k−1+Kk(yk−Hk{circumflex over (x)}k|k−1){circumflex over (x)}k+1|k={circumflex over (x)}k|k  (3)Kk={circumflex over (P)}k|k−1HkT(1+Hk{circumflex over (P)}k|k−1HkT)−1  (4){circumflex over (P)}k|k={circumflex over (P)}k|k−1−KkHk{circumflex over (P)}k|k−1 
                                          P            ^                                              k              +              1                        |            k                          =                                            P              ^                                      k              |              k                                +                                                    σ                ω                2                                            σ                υ                2                                      ⁢            I                                              (        5        )            where,{circumflex over (x)}k|k=[ĥ0[k], . . . , ĥN−1[k]]T, Hk=[uk−1, . . . , uk−N]{circumflex over (x)}0|−1=0, {circumflex over (P)}0|−1=ε0I, ε0>0  (6)Here, the impulse response {hi} of unknown system is obtained as a state estimate x^k|k, and an input {uk} to the system is used as an element of an observation matrix Hk.
Fast Kalman filtering algorithm is also known, which reduces the amount of calculation per unit time step to the number of times calculations are performed proportional to N, that is, O(N) by applying the shift property (Hk+1(i+1)=Hk(i)) of the observation matrix Hk to a Kalman filter obtained when σ2w=0. Details are written in “Digital Signal Processing Handbook”, the Institute of Electronics, Information and Communication Engineers, 1993, or the like.
(Applications to Echo Cancellers)
Four-wire circuits are used for long distance telephone lines such as for international calls for a reason of signal amplification and others. On the other hand, two-wire circuits are used for subscriber lines because they are relatively short.
FIG. 16 is an explanation view of a communication system and an echo. Impedance matching is performed by disposing hybrid transformers at connection points between two-wire circuits and a four-wire circuit, as shown in the figure. If the impedance matching is perfect, a signal (voice) from a speaker B reaches only a speaker A. However, it is difficult to make the matching perfect in general. A phenomenon occurs in which a part of a received signal leaks to the four-wire circuit, is amplified, and returns to the receiver (speaker A). This is an echo. As the transmission distance gets longer (delay time gets longer), the effect of the echo gets larger, and the quality of telephone speech significantly deteriorates (in pulse transmission, an echo influences significantly even in a short distance, and the quality of telephone speech deteriorates). FIG. 17 shows a basic principle of an echo canceller.
As shown in the figure, the echo canceller is introduced to successively estimate the impulse response of an echo path by using a received signal and an echo directly observable, and to subtract a quasi echo obtained by using the estimate from an actual echo to cancel and remove the echo.
The impulse response of the echo path is estimated such that the mean square error of a residual echo ek is minimized. Elements which disturb the estimation of the echo path are line noise and a signal (voice) from the speaker A. When two speakers start talking at the same time (double talking), the estimation of the impulse response is generally halted. Since the impulse response of the hybrid transformers has a length of approximately 50 [ms], if the sampling period is set to 125 [μs], the order of the impulse response of the echo path actually becomes approximately 400.